1. Field of the Invention
The present invention generally pertains to battery power management and more particularly to a method of providing a correct approximation for the dynamic state-of-charge within a battery subject to dynamic charging and discharging.
2. Description of the Background Art
The tracking of battery energy is crucial within a variety of battery power management systems, such as those employed within internal-combustion and electric vehicles. Battery power management systems control the charging and/or discharging of a battery pack through a given load. In many of these applications, as typified by the electrical system of an internal combustion automobile, the battery is dynamically cycled between charging and discharging. During charging, it is important to track the battery energy to determine the optimum rate at which to charge the battery. During battery discharge it is important to recognize the relative amount of capacity remaining. Numerous drawbacks exist within typical methods utilized for battery energy tracking of a battery subject to charge/discharge cycling.
Batteries are typically charged at a variable rate, owing to the fact that rechargeable batteries can accept a higher charge current when fully depleted than when approaching a state of full-charge. A critical metric used within charging systems is that of a desired charge profile for a given battery type which specifies charge rate under a given set of conditions. A charge rate which is inadequate under a set of given circumstances increases the charge time, while a charge rate which is excessive under the given set of circumstances causes increased out-gassing and a reduction in battery longevity. Numerous charging methods have been used, therefore, to provide a charge rate suitable to the battery and its proper charging profile. For example, constant current chargers typically provide for a maximum charge current within a limited voltage, such that the current drops off as the battery approaches the upper voltage limit of the charger output. Determining a proper charging profile, however, is replete with conditional variables which increase complexity, and is further complicated by dynamic charging/discharging. However, it has been difficult to create advanced charging mechanisms that are more capable of properly charging the battery due in part to the difficulty with determining the current charge state of the battery. This is because the optimum charge rate of a battery may be considered largely dependent on its state-of-charge (SOC). A simple definition for state-of-charge (SOC) can be expressed as: ##EQU1##
where Q.sub.r is the remaining capacity of the battery under the reference condition, and Q.sub.n is the nominal capacity of the battery (typically measured in ampere-hours, Ah) under test. Although, the concept of state-of-charge is relatively simple, the correct implementation is complicated as the determination of factors Q.sub.r and Q.sub.n require an in-depth understanding of the static and dynamic behavior within the battery. In literature on chargers and battery systems, it is common to find an algorithm which combines a set of multiple SOC definitions that are somehow bundled together to provide a final SOC calculation method. For instance, many investigators estimate the change in SOC by performing a simple current-time integration method such that ##EQU2##
where i is the charge or discharge current (in amperes, A), and .DELTA.t is the time interval (in hours, h) and Q.sub.i is the battery capacity (ampere-hours, Ah) as determined at discharge current i. The calculation of SOC is thereby often given by: EQU SOC=SOC+.DELTA.SOC (3)
However, use of this combination approach is fundamentally and mathematically erroneous and it provides no physical meaning. The summation of Eq. (1) and Eq. (2) into Eq. (3) is mathematically incompatible as these two equations describe two different fractions. The fraction of remaining capacity in terms of the nominal capacity is represented by Eq. (1), for instance based on a 20-hour rate, or C.sub.20, while the fractional change in current-dependent capacity during the time interval is represented by Eq. (2). No physical information is provided by Eq. (3) as defined in Eq. (1) because one is unable to predict "remaining capacity" from the newly calculated SOC. In addition, any reference to the so-defined SOC function must be further quantified by specifying the discharge rate along with temperature.
A correlation has in other instances been derived in response to the Peukert equation: EQU Q.sub.p =i.sup.n t (4)
where Q.sub.p is the characteristic battery capacity, n is the battery discharge rate sensitivity exponent, and t is the duration of discharge to specify an end-of-discharge condition. Therefore, the dynamics of Eq. (2) may be re-written as ##EQU3##
in order to incorporate the effect on capacity variation for different discharge currents according to the Peukert model. The resultant model assumes that the total increase, or decrease, in capacity (as determined by constant-current discharge) is directly proportional to the infinitesimal changes in usable capacity under dynamic conditions. In practice, this approach is widely accepted because of its ease of implementation even though it fails to relate the battery dynamics with the fundamental prediction of "remaining capacity" (or SOC). As a result, Eq. (5) is also mathematically inconsistent having Q.sub.p expressed in different units. ([Amp].times.[hour]) is equated with [Amp].sup.n.times.[hour]). The Peukert model has also been found experimentally to provide an inadequate approach to accurately determining SOC within a dynamic system.
Therefore, a need exists for a method of properly determining, and/or maintaining state-of-charge (SOC) information for a battery being charged or discharged. The present invention satisfies that need, as well as others, and overcomes the deficiencies of previously developed charger solutions.